Question : If $\tan A \tan B+\frac{\cos x}{\cos A \cos B}=1$, then $x=?$
Option 1: $B$
Option 2: $A$
Option 3: $A + B$
Option 4: $A - B$
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Correct Answer: $A + B$
Solution :
$\tan A \tan B+\frac{\cos x}{\cos A \cos B}=1$
⇒ $\tan A \tan B \cos A \cos B + \cos x = \cos A \cos B$
⇒ $\sin A \sin B + \cos x = \cos A \cos B$
⇒ $ \cos x = \cos A \cos B - \sin A \sin B$
⇒ $ \cos x = \cos (A+B) $
⇒ $ x = A+B$
Hence, the correct answer is $A + B$.
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